Today more details are available. T-Mobile's version of the Galaxy Mini will be called Samsung Dart, and the official imagery has leaked to CellPhoneSignal. Here it is in all its glory:
According to the same source, June 15 will indeed be when this phone hits the (US) streets. The Dart will come in one color version – gray – as seen above. It will have a QVGA (240×320) touchscreen, a 2 MP camera with no flash, 3G, and Bluetooth. The Dart will run Android 2.2 Froyo when it launches.
source: Unwired View